This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A209618 #19 Jan 09 2025 02:22:17 %S A209618 139,181,241,283,337,409,421,547,577,631,691,709,787,811,829,919,1021, %T A209618 1039,1051,1129,1153,1171,1249,1327,1399,1471,1627,1699,1723,1801, %U A209618 1831,1879,1933,1951,2017,2029,2053,2089,2113,2143,2221,2251,2311,2477,2521,2557 %N A209618 Primes separated from their adjacent next primes by a composite number of successive composites. %C A209618 Primes prime(k) such that A046933(k) is composite. - _Robert Israel_, Jan 08 2025 %H A209618 Robert Israel, <a href="/A209618/b209618.txt">Table of n, a(n) for n = 1..10000</a> %e A209618 a(1) = 139 is the first prime separated from the next prime (149) by a composite number (9) of successive composites, namely, 140, 141, 142, 143, 144, 145, 146, 147, 148. %p A209618 P:= select(isprime,[seq(i,i=3..3000,2)]): %p A209618 G:= P[2..-1]-P[1..-2]-~1: %p A209618 J:= remove(t -> G[t]=1 or G[t]::prime, [$1..nops(G)]): %p A209618 P[J]; # _Robert Israel_, Jan 08 2025 %t A209618 ps = Prime[Range[500]]; pos = Position[Differences[ps] - 1, _?(# > 1 && ! PrimeQ[#] &)]; ps[[Flatten[pos]]] (* _T. D. Noe_, Mar 21 2012 *) %Y A209618 Cf. A046933, A209619. %K A209618 nonn %O A209618 1,1 %A A209618 _Lekraj Beedassy_, Mar 21 2012